Multiply the following complex numbers: $({-1+i}) \cdot ({4+3i})$
Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({-1+i}) \cdot ({4+3i}) = $ $ ({-1} \cdot {4}) + ({-1} \cdot {3}i) + ({1}i \cdot {4}) + ({1}i \cdot {3}i) $ Then simplify the terms: $ (-4) + (-3i) + (4i) + (3 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ -4 + (-3 + 4)i + 3i^2 $ After we plug in $i^2 = -1$ , the result becomes $ -4 + (-3 + 4)i - 3 $ The result is simplified: $ (-4 - 3) + (1i) = -7+i $